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Theorems · Theorem · order theory

Order.lt_succ_iff_eq_or_lt

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] {a b : α} [NoMaxOrder α],
  a < Order.succ b ↔ a = b ∨ a < b
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
2 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrderNoMaxOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ordinal.veblenWith_add_one · cited by 3Ordinal.veblenWith_add_oneOrder.lt_succ_iff_eq_or_gt · cited by 0Order.lt_succ_iff_eq_or_gtLinearOrder · cited by 8572LinearOrderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderNoMaxOrder · cited by 340NoMaxOrderOrder.lt_succ_iff · cited by 22Order.lt_succ_iffle_iff_eq_or_lt · cited by 20le_iff_eq_or_ltOrder.lt_succ_iff_eq_or_ltCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.